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A088732 First prime in the arithmetic progression n+k*(n+1) with k>0.

%I A088732 #27 Feb 16 2025 08:32:51
%S A088732 2,3,5,7,19,11,13,23,17,19,43,23,103,41,29,31,67,53,37,59,41,43,137,
%T A088732 47,149,103,53,83,173,59,61,127,131,67,139,71,73,113,233,79,163,83,
%U A088732 257,131,89,137,281,191,97,149,101,103,211,107,109,167,113,173,353,179
%N A088732 First prime in the arithmetic progression n+k*(n+1) with k>0.
%H A088732 T. D. Noe, <a href="/A088732/b088732.txt">Table of n, a(n) for n = 0..10000</a>
%H A088732 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DirichletsTheorem.html">Dirichlet's Theorem</a>
%H A088732 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LinniksTheorem.html">Linnik's Theorem</a>
%H A088732 Wikipedia, <a href="http://en.wikipedia.org/wiki/Linnik%27s_theorem">Linnik's theorem</a>
%H A088732 <a href="/index/Pri#primes_AP">Index entries for sequences related to primes in arithmetic progressions</a>
%e A088732 For n=10, the progression starts: 10, 21, 32, 43, 54, 65, 76, 87, 98, 109, etc., 43 is the first prime: a(10)=43.
%t A088732 Table[k = 1; While[p = n + k*(n + 1); ! PrimeQ[p], k++]; p, {n, 0, 100}] (* _Frank M Jackson_, Oct 20 2011 *)
%o A088732 (Haskell)
%o A088732 a088732 n = head [q | q <- [2 * n + 1, 3 * n + 2 ..], a010051' q == 1]
%o A088732 -- _Reinhard Zumkeller_, Oct 01 2014
%o A088732 (Python)
%o A088732 from itertools import accumulate, repeat
%o A088732 from sympy import isprime
%o A088732 def A088732(n): return next(m for m in accumulate(repeat(n+1),initial=(n<<1)+1) if isprime(m)) # _Chai Wah Wu_, Aug 02 2023
%Y A088732 Cf. A088733.
%Y A088732 Cf. A010051.
%K A088732 nonn
%O A088732 0,1
%A A088732 _Reinhard Zumkeller_, Oct 12 2003